Finite Type Link Homotopy Invariants

Abstract

Bar-Natan used Chinese characters to show that finite type invariants classify string links up to homotopy. In this paper, I construct the correct spaces of chord diagrams and Chinese characters for links up to homotopy. I use these spaces to show that the only rational finite type invariants of link homotopy are the pairwise linking numbers of the components.

15 pages, many figures. Revised to acknowledge work of Bar-Natan, Garoufalides, Rozansky and Thurston. Revised again to clarify the exposition in section 4

References in corpus (2)

• The number of primitive Vassiliev invariants up to degree 12
• The Aarhus integral of rational homology 3-spheres II: Invariance and universality